question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
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<p>The problem: A car with a mass of 1200 kg and speed 10 m/s runs into a traffic barrier at an angle of 45 degrees, and is thrown outwards at an angle of 45 degrees relative to the barrier with a speed of 5.0 m/s How big was the change in momentum of the car during the collision?</p>
<p>I tried decomposing the momentum, but failed to get the right answer. Can someone explain to me how I can solve this question without using the fact that Pinitial and Pfinal make a right triangle?</p>
<p>Additionally, someone made the following solution to this problem:</p>
<p>$$\vec{p_e} = 1200 kg \cdot 5 m/s [{1 \over \sqrt{2}} , {1 \over \sqrt{2}}] \\
\vec{\Delta p} = \vec{p_e} - \vec{p_f} = 1200 [-{5 \over \sqrt{2}}, {15 \over \sqrt{2}}] kg m/s \\
|\vec{\Delta p}| = 1200 \sqrt{({5 \over \sqrt{2}})^2 + ({15 \over \sqrt{2}})^2} kg m/s = 1,3 \cdot 10^4 kgm/s$$</p>
<p>Can someone please explain to me how vectors and trig are used to solve this? I especially don't understand what the following means, and where it came from: $$[{1 \over \sqrt{2}} , {1 \over \sqrt{2}}] \\$$</p> | g10740 | [
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<p>A ladder $AB$ of mass $m$ has its ends on a smooth wall and floor (see figure). The foot of the ladder is tied by an inextensible rope of negligible mass to the base $C$ of the wall so the ladder makes an angle $\alpha$ with the floor. Using the principle of virtual work, find the magnitude of the tension in the rope. </p>
<p>My equations:</p>
<p>I assume length of ladder = $L$</p>
<p>$x$-direction: $$N_2 = mg$$</p>
<p>$y$-direction: $$N_1 = T$$</p>
<p>torque equation about $B$: $$ T_{about B}=T_{mg}+T_{A} = \frac{L}{2}(mg)cos\alpha-LN_1 sin\alpha=0$$
Therefore, $$\frac{L}{2}(mg)cos\alpha-LT sin\alpha=0$$</p>
<p>And we get $$T= \frac{1}{2}(mg)cot\alpha$$</p>
<p>which is the answer. </p>
<p>However, I am supposed to find this using the principle of virtual work. To do this, I guess I would have to displace the ladder downward at $A$ and rightward at $B$, in which case the normal forces $N_1$ and $N_2$ do no work. I then conclude that the work done by the gravitational force $mg$ along the downward displacement of the center of mass of the ladder counterbalances the tension times the horizontal displacement at $B$. However, finding the displacement of the center of the ladder as the ladder slides downwards doesn't seem to be an easy task, so I must be on the wrong track. The final equation I have to deal with seems to be $$mg.\delta y_{com}-T.\delta x_{at B}=0$$</p>
<p>Any inputs would be appreciated. </p>
<p><img src="http://i.stack.imgur.com/yhIPX.jpg" alt="enter image description here"></p> | g10741 | [
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<p>I just cooked a meat pie in the oven. Almost immediately after pulling it out of the oven, I felt that the crust was only slightly warm, but when I cut it open the filling felt very warm. I can't understand how the crust could be at a lower temperature. My understanding was that the oven heats the air, then the air heats the crust and the crust heats the filling inside. As long as the air is hotter than the crust (should be always), there is no way for the crust to lose heat, except by heating the filling and there is no way for the filling to gain heat, without being heated by the crust. According to this logic, the filling can't be hotter than the crust. Given this situation, why does the filling feel hotter than the crust?</p> | g10742 | [
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<p>This is a nice problem that I would like to share. </p>
<p><strong>Problem:</strong> In a public garden, there a statue consisting of a spherical stone and a stone cup. The ball is 1 meter in diameter and weighs at least a ton. The cup is an upside-down hemispherical shell, and the ball sits in this shell and fits it almost exactly. Water is pumped into the bottom of shell so that a thin film exists between shell and the ball. The result is a ball that is free to rotate with negligible friction.</p>
<p>You only have access to the ball near the top, so while you can push it to make it turn around any horizontal axis, you can't get enough of a grip to make it turn around the vertical axis. Can you impart a net angular momentum around the vertical axis anyway, so that the balls spins around the vertical axis?</p>
<p><strong>Source:</strong> <em>Vector Calculus, Linear Algebra, and Differential Forms</em> by Hubbard and Hubbard. </p> | g10743 | [
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<p>Radiation is basically just particles flying around, right? Are free hydrogen atoms just typically not moving fast enough to be considered "radiation"?</p> | g10744 | [
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<p>This post is inspired by this <a href="http://math.stackexchange.com/questions/302023/best-sets-of-lecture-notes-and-articles">math.se post</a>.</p>
<p>Let me start by apologizing if there is another thread on phys.se that subsumes this.</p>
<p>I often find that I learn best from sets of lecture notes and short articles. There are three particular reasons that make me feel this way.</p>
<ol>
<li><p>Lecture notes and articles often times take on a very delightful informal approach. They generally take time to bring to the reader's attention some interesting side fact that would normally be left out of a standard textbook (lest it be too big). Lecture notes and articles are where one generally picks up on historical context, overarching themes (the "birds eye view"), and neat interrelations between subjects.</p></li>
<li><p>It is the informality that often allows writers of lecture notes or expository articles to mention some "trivial fact" that every textbook leaves out. Whenever I have one of those moments where a definition just doesn't make sense, or a theorem just doesn't seem right it's invariably a set of lecture notes that sets everything straight for me. People tend to be more honest in lecture notes, to admit that a certain definition or idea confused them when they first learned it, and to take the time to help you understand what finally enabled them to make the jump.</p></li>
<li><p>Often times books are very outdated. It takes a long time to write a book, to polish it to the point where it is ready for publication. Notes often times are closer to the heart of research, closer to how things are learned in the modern sense.</p></li>
</ol>
<p>It is because of reasons like this that I find myself more and more carrying around a big thick manila folder full of stapled together articles and why I keep making trips to Staples to get the latest set of notes bound.</p>
<p>So, if anyone knows of any set of lecture notes, or any expository articles that fit the above criteria, please do share!</p>
<p>I'll start:</p>
<p><strong>People/Places who have a huge array of fantastic notes:</strong></p>
<p><a href="http://www.staff.science.uu.nl/~hooft101/theorist.html">'t Hooft</a></p>
<p><a href="http://math.ucr.edu/home/baez/QG.html">John Baez</a></p>
<p><br />
<b>The <i>Feynman </i>lectures on Physics:</b><br /></p>
<li><a href="http://www.feynmanlectures.caltech.edu/I_toc.html">The Feynman Lectures on Physics, Volume I: mainly mechanics, radiation, and heat.</a> </li>
<li><a href="http://www.feynmanlectures.caltech.edu/II_toc.html">The Feynman Lectures on Physics, Volume II: mainly electromagnetism and matter.</a></li>
<li><a href="http://www.feynmanlectures.caltech.edu/III_toc.html">The Feynman Lectures on Physics, Volume III: quantum mechanics.</a></li>
<p>
<br />
<b>Introductory Courses</b><br />
<br /></p>
<ul>
<li><b>Introductory Classical Mechanics</b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/301/301.pdf</li>
<li>http://space.wccnet.edu/~gkapp/</li>
<li>http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/</li>
<li>http://academics.smcvt.edu/abrizard/Classical_Mechanics/Notes_070707.pdf</li>
<li>http://www.maths.tcd.ie/~dleen/mathsoc/pdf/Notes.pdf</li>
</ol>
<p><br /></p>
<ul>
<li><b>Optics and Thermodynamics & Electromagnetism</b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/316/316.pdf</li>
<li>http://seagull.ukzn.ac.za/~mukaror/</li>
<li>http://www.sicyon.com/resources/library/pdf/optics.pdf</li>
</ol>
<p><br /></p>
<ul>
<li><b>Waves and Oscillations </b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/315/Waves.pdf</li>
<li>http://www.ma.hw.ac.uk/~bernd/F12MS3/</li>
<li>http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/OscWavesIndex.htm</li>
</ol>
<p><br /></p>
<ul>
<li><b>Statistical Mechanics and Thermodynamics</b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/sm1/statmech.pdf</li>
<li>http://www.spms.ntu.edu.sg/PAP/courseware/statmech.pdf</li>
<li>http://www.physics.umd.edu/courses/Phys603/kelly/</li>
<li>http://stp.clarku.edu/notes/</li>
</ol>
<p><br /></p>
<ul>
<li><b>Electronics</b></li>
</ul>
<ol>
<li>http://openbookproject.net/electricCircuits/</li>
<li>http://ocw.mit.edu/courses/music-and-theater-arts/21m-380-music-and-technology-live-electronics-performance-practices-spring-2011/lecture-notes/</li>
<li>http://zebu.uoregon.edu/~rayfrey/432/DigitalNotes.pdf</li>
<li>http://courseware.ee.calpoly.edu/~jzhang/EE112/</li>
<li>http://www-inst.eecs.berkeley.edu/~ee130/sp07/lecture.html</li>
<li>http://www.engr.sjsu.edu/kghadiri/EE122/Class_notes.htm</li>
<li>http://www.cramster.com/course-introduction-lecture-note-r30-6638.aspx</li>
</ol>
<p><br /></p>
<ul>
<li><b>Computational Physics</b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/329/329.pdf</li>
<li>http://www.physics.umd.edu/courses/CourseWare/EssentialMathematica/</li>
<li>http://www.cmth.ph.ic.ac.uk/people/a.mackinnon/Lectures/compphys/</li>
<li>http://math.fullerton.edu/mathews/numerical.html</li>
</ol>
<p><br /></p>
<ul>
<li><b>Introductory Quantum Mechanics</b></li>
</ul>
<ol>
<li>http://farside.ph.utexas.edu/teaching/qmech/qmech.pdf</li>
<li>http://galileo.phys.virginia.edu/classes/252/home.html</li>
<li>http://walet.phy.umist.ac.uk/QM/QM.pdf</li>
<li>Video: http://physicsstream.ucsd.edu/courses/spring2003/physics130a/</li>
<li>http://quantummechanics.ucsd.edu/ph130a/130_notes.pdf</li>
<li>http://www.lecture-notes.co.uk/susskind/quantum-entanglements/</li>
</ol>
<p><br /></p>
<ul>
<li><b>Classical And Quantum Optics</b></li>
</ul>
<ol>
<li>http://people.seas.harvard.edu/~jones/ap216/lectures/lectures.html</li>
<li>http://atomoptics.uoregon.edu/~dsteck/teaching/optics/</li>
</ol>
<p><br />
<br />
<br /></p>
<p>(from my Blog <a href="http://quantizd.blogspot.com">http://quantizd.blogspot.com</a>)</p>
<p>So my goal is to ameliorate this list by adding more resources.</p>
<p>Thank you.</p> | g10745 | [
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<p>I'm having trouble understanding the surface used for <a href="http://en.wikipedia.org/wiki/Amp%C3%A8re%27s_circuital_law" rel="nofollow">Ampere's Circuital Law</a>. In classes, we've been using simple circular or rectangular loops. Is the surface supposed to be area of the circle or the rectangle? Or is it a simple case of the law? </p>
<p>A example would be the surface used for displacement current. This one is just lost on me. The surface looks like a pot enclosing the wire and the capacitor. Does the law specify a closed loop of a surface? Is the line integral taken on the mouth of the pot-like surface or the bottom ($S_1$ below)? And is the enclosed current in the smaller mouth or the larger bottom surface ($S_2$)?</p>
<p><img src="http://i.stack.imgur.com/5Rlor.jpg" alt="enter image description here"></p> | g10746 | [
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<p>The <a href="http://en.wikipedia.org/wiki/Random_phase_approximation" rel="nofollow">random phase approximation</a> (RPA) is an approximation method in condensed matter physics and in nuclear physics. </p>
<p>What is the difference between RPA and generalized RPA?</p> | g10747 | [
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<p>I'm doing some homework in Classical Mechanics, and is about to write out the Lagrangian of a system. But, when I check the answer from my teacher, something is missing.</p>
<p>The kinetic energy I'm using is given by:</p>
<p>$$T =\frac{1}{2}m\dot{x_{m}}^{2},$$</p>
<p>where</p>
<p>$$\dot{x_{m}} = \dot{x}+L \cos(\phi)\dot{\phi}$$</p>
<p>Now, when I want to write out the entire Lagrangian I need to expand the squared $\dot{x_{m}}$, which in my calculations give me the following:</p>
<p>$$\frac{1}{2}m(\dot{x}^{2}+2\dot{x}L \cos(\phi)\dot{\phi}+L^{2} \cos^{2}(\phi)\dot{\phi}^{2})$$</p>
<p>But apparently, according to the solution, the $\cos^{2}(\phi)$ term becomes $1$, and only $L^{2}\dot{\phi}^{2}$ is left.</p>
<p>So my question is: Why is that? I've been checking around, but nothing I find makes it one. I know that $\cos^{2}(\phi) = \frac{1}{2}(1+\cos(2\phi))$, but that doesn't seem to help me either.</p> | g10748 | [
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<p>The Beer-Lambert law is: $ I=I_{0}e^{-n\sigma(\lambda) x} $,
where $ n $ is the volume concentration and $ \sigma $ the "efficient" cross-section.</p>
<p>For interaction with F-centers (kind of crystal defects: electrons trapped in negative ions lakes), what is the boundary effect on the exponential parameter: $ n\sigma(\lambda) $ ?</p>
<p>Thank you.</p> | g10749 | [
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<p>It has been stated <a href="http://physics.stackexchange.com/a/100719">here</a> that:
<blockquote>we can say, without introducing a coordinate system, that the interval associated with two events is <em>timelike</em>, <em>lightlike</em>, or <em>spacelike</em></blockquote>.</p>
<p>This assertion appears at variance with </p>
<ul>
<li><p>the definition of "<i>time-like (or light-like, or space-like) intervals</i>" as defined here: <a href="http://en.wikipedia.org/wiki/Spacetime#Spacetime_intervals" rel="nofollow">http://en.wikipedia.org/wiki/Spacetime#Spacetime_intervals</a> explicitly in terms of "<i>differences of the space and time coordinates</i>", and</p></li>
<li><p>the definition of "<i>curves</i>" as "<i>chronological (or timelike)</i>", "<i>null</i>" (or "lightlike"), or "<i>spacelike</i>", and thus correspondingly of pairs of "<i>points</i>" of any such "<i>curve</i>" as "<i>timelike (or lightlike, or spacelike)</i> related to each other" of <a href="http://en.wikipedia.org/wiki/Causal_structure#Curves" rel="nofollow">http://en.wikipedia.org/wiki/Causal_structure#Curves</a> which explicitly requires the notion of <a href="http://en.wikipedia.org/wiki/Lorentzian_manifold#Lorentzian_manifold" rel="nofollow">Lorentzian manifold</a> and thus according to <a href="http://en.wikipedia.org/wiki/Manifold#Mathematical_definition" rel="nofollow">http://en.wikipedia.org/wiki/Manifold#Mathematical_definition</a> uses coordinates as subsets of $\mathbb R^n$ and their topological relations (as "<i>coordinate system</i>"). </p></li>
</ul>
<p>Therefore I'd like to know:<br>
How can be determined whether the interval associated with two events (which are given or characterized and distinguished by naming, for either event, the distinct individual participants which had been coincident at that event) is for instance "<i>timelike</i>", <b>without</b> using any coordinates and coordinate system?</p>
<p>Is it correct that the interval associated with two events (given as described above) is "<i>timelike</i>" if and only if there exists at least one participant who took part in both of these events?</p> | g10750 | [
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<p>I've been reading a lot but cannot find an example of 2D Gaussian wave packet moving in a particular direction. I've done some of the math myself, in a 1D case, and then kind of guessed the generalization to 2D. I'd be thrilled if someone could confirm or correct the expression. This is supposed to model a free particle moving in the x axis with a fairly definite momentum:</p>
<p>$\Psi (x,y,t) = \frac{1}{\sqrt{\alpha + i\beta t}} \exp \left[-\dfrac{(x-vt)^2+y^2}{4(\alpha + i\beta t)} + i(kx-\omega t) \right] $</p>
<p>The wave function is not normalized and the constants $\alpha$ and $\beta$ are not relevant in my opinion, I could add how they relate with mass and $\hbar$ if someone thinks they're necessary. </p>
<p>Also I would like to add to the question what's the relation between $k$, $\omega$ and $v$ and what does each one represent. My guess is that $v$ is the group velocity, and you'd get the average momentum from the fourier transform of that wave function, but I'm not sure what's $k$ then. Is there any need at all to add the phasor $e^{i(kx-wt)}$, does it change anything?? The packet is going to move anyway and the amplitude is not going to change unless you add other wave functions. </p>
<p>Thank you very much!</p> | g10751 | [
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<p>Me and my friend, both many years from learning string theory, had a recent debate about it anyway. He said he already partially discounts it because after learning waves, he believes any function, and thus any kind of physical process can be created through a superposition of an infinite sum of waves. Since string theory to our understanding is made up of primarily oscillating strings, he argues that it is a mathematical necessity for string theory to create equations for the physical world, regardless of whether the theory actually is "true" or not. </p>
<p>My understanding is that Fourier analysis can only create arbitrary periodic functions, can it in principal create any real world field or particle, etc.? Besides this, I argued that this might be a pointless question anyway, as if we can create a perfect model of the universe with string theory, then the question of whether the universe is really made of oscillating strings is more of a philosophical question that may not mean anything at all.</p>
<p>Through reading Brian Green's books I know that M-theory at least incorporates more than just strings, but I have no clue as to how things such as branes work, can his argument even apply to these other fundamental objects in string theory?</p>
<p>So my question is, is Fourier Analysis essentially what String Theory is? And if so, does that make it any less of a true physical theory of the universe?</p> | g10752 | [
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<p>Well I've been asked this question, but I haven't been able to come with an answer yet using books and some web searches. The point is as the title says, to answer the question with the whole phenomenon explanation if possible. </p> | g10753 | [
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0.012108871713280678,
0.0252273790538311,
0.03565332666039467,
-0.054582562297582626,
-0.03348344936966896,
-0.01308309007436037,
0.07994057238101959,
0.019373... |
<p>I read in a book that for $\beta$-decay the electrons have always been found to have an expectation value for their helicity of $h=-v/c$. </p>
<p>Then ist is said in the book, that it follows from this fact that such electrons are in a left-handed chiral state which is characteristic for the weak interaction.</p>
<p>In another article I read that the chiral state of an electron is not conserved in time. The electron will soon evolve a component with a right-handed chiral state and it will be a mixture of right- and lef-handed chiral states.</p>
<p>Suppose after the decay one electron moves like a free particle.<br>
When it evolves a right-handed chiral component in addition to the left-handed component it starts off with, how can its helicity be conserved?</p> | g10754 | [
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<p>I am quite interested in the understanding of the relation between p_ip wave superconductor(SC) and the Moore-Read(MR) state.</p>
<p>They share many similar properties, for example, p+ip SC has majorana as vortex excitation, MR has nonabelian quasi hole excitation. More interestingly, their wavefuncions are similar to some extent. All of them can be found in Read and Green's paper: <a href="http://arxiv.org/pdf/cond-mat/9906453v3.pdf" rel="nofollow">http://arxiv.org/pdf/cond-mat/9906453v3.pdf</a>. (where you can find the wavefunction for p+ip SC in eqn.12 and above, MR wavefunction in eqn.5.1 in <a href="http://www.physics.rutgers.edu/~gmoore/MooreReadNonabelions.pdf" rel="nofollow">http://www.physics.rutgers.edu/~gmoore/MooreReadNonabelions.pdf</a>).</p>
<p>These two wave functions are similar only when electrons are separated far from each other, as shown in eqn 16 in Read Green's paper.</p>
<p>Does anyone know how to explain the relation between these two states? Why they share similar property at long distance?</p>
<p>Thanks in advance.</p> | g10755 | [
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<p>I don't understand why there is necessarily a diffraction limitation on optical systems. Where does this limitation in focusing light come from? </p> | g10756 | [
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<p>I have an 134.2 khz RFID antenna for sport events which is basically a 1x1 meter square sheet of rubber with 3 loops of antenna cable embedded. The problem is that the transponder recognition range is drastically reduced when the ground below the antenna contains metal (e.g. reinforced concrete).</p>
<p>Would it be possible to solve this problem by attaching a layer of mu-metal or permalloy to the lower side of the antenna? I read that mu-metal draws magnetic field lines into itself and thus redirects them around what's behind (in this case the metal in the ground). Would this make sure that the magnetic field on the upper side of the antenna is the same as if there was no metal in the ground? (and that the transponder recognition range is as good as without the metal) What thickness of the material would be required, would a foil be sufficient?</p> | g10757 | [
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<p>I've been asking myself a question for quite some time :</p>
<ul>
<li>say that a bullet gets out of a gun at 900 km/h (I'm european, hence the metric system).</li>
<li>say a train could go in a straight line at 900 km/h</li>
<li>say you're at the back of that train, and you'd shoot a bullet backwards. The bullet exits your gun at 900km/h and flies away from the train at the same speed.
However, what would happen for an earth observer?</li>
</ul>
<p>You'll agree that if you shoot in an open field, the bullet will stay at the same altitude for several seconds before falling to the ground (with a field large enough).
So from that train, same thing applies.
So for the earth observer, the bullet will not have an horizontal speed, and will stay at the same altitude for several seconds before falling to the ground.
So basically it'll float up in the air without falling. That'd be strange for the earth observer, right?</p>
<p>But the horizontal speed will decrease of course.
So for the earth observer, the bullet will, for a few seconds, stay still at the same position, and then after several seconds will start to fall down a little bit, and will start to move towards the train, because its horizontal speed towards the train will decrease. Strange again!</p>
<p>OK last one: what would happen if the earth observer tried to catch the bullet with his bare hands? Nothing right? Just maybe a very hot bullet because of the explosion but it'd be basically as easy to catch as a stone floating up in the air?
And don't tell me that the bullet will slow down due to air friction, because remember the bullet is not moving. Or very slowly.</p> | g10758 | [
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<p>As can for example be learned from chapter I.2 of Anthony Zee's <em>Quantum field theory in a nutshell</em>, path integrals can be used to to calculate the amplitude for a system to transition from one state to another by considering all possible paths between the two states.</p>
<p><a href="http://motls.blogspot.com/2012/11/when-truths-dont-commute-inconsistent.html?m=1" rel="nofollow">This</a> article gives a nice technical introduction to <a href="http://en.wikipedia.org/wiki/Consistent_histories" rel="nofollow">consistent histories</a> and explains that this method can be used to calculate the answer to questions about alternative histories in a consistent set. For two histories to be consistent, their probabilities must be mutually exclusive such that their probabilities are "additive".</p>
<p>Looking at these two methods to calculate answers to meaningful questions in quantum mechanics (and how the relevant formulas are derived), they seem very similar to me. </p>
<p>So my question is:</p>
<p>What is the exact relationship between the method of path integral and consistent histories? Could one say that the consistent histories are some kind of the "classical limit" of the path integrals? Or does coarse graining (by an appropriate method?) Feynman's path integrals lead to consistent histories as a limit (IR fixed point)?</p>
<p>(In the article about the consistent histories it is mentioned, that if one considers too fine grained histories, they are due to the uncertainty principle no longer consistent and would resemble Feynman's path integrals. But I'd like to see an extended technical / mathematical explanation of the relationship between the two things to really understand it.)</p> | g10759 | [
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<p>Are there any non magnetic materials that attract to each other as if they were magnetic?</p>
<p>This is an argument I am having with a friend. </p>
<p>Thanks,</p> | g10760 | [
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<blockquote>
<p>Point A moves uniformly with velocity $v$ so that the vector $\vec{v}$ is continually "aimed" at point B which in turn moves rectilinearly and uniformly with velocity $u < v$. At the initial moment $\vec{v} \perp \vec{u}$ and the points are separated by a distance $l$. How soon will the points converge?</p>
</blockquote>
<p>This seemed a very daunting problem at first, but then I tried to break it down with some calculus:</p>
<p>Consider a coordinate system such that $A$ moves along positive $y$ axis and $B$ along positive $x$.Let the particles meet at time $T$.</p>
<p>At an aribitrary time $t = t_0$, the velocity of the particle is inclined at an angle $\theta$ to the horizontal, so the horizontal component of the velocity is $v\cos\theta$. Displacement in a small time interval $dt$ at $t_0$ along the $x$ axis (along direction of motion of $B$) is:</p>
<p>$$v\cos\theta\ dt$$</p>
<p>Summing from $0$ to $T$. The displacement along $x$ axis of particle $A$ equals $uT$.</p>
<p>$$\int_0^T v\cos\theta\ dt= uT \implies \int_0^T\cos\theta \ dt = \frac{uT}{v} \tag1$$</p>
<p>Similarly, for the displacement along the $y$-axis:</p>
<p>$$\int_0^T\sin\theta\ dt = \frac{l}{v} \tag2$$</p>
<p>I'm not sure how to solve these equations, and I'm not sure if the solution is possible either using my method. How do I go about the problem?</p>
<p>I went over the solutions that have been written on other websites. Most of them first establish the same thing I did in the first step</p>
<p>$$\int_0^T \cos\theta \ dt = \frac{uT}{v}$$</p>
<p>Its the second step I don't understand. At time $t$, </p>
<p><img src="http://i.stack.imgur.com/RsPU5.png" alt="enter image description here"></p>
<p>It is claimed that at time $t$:</p>
<p>$$\frac{dr}{dt} = v - u\cos\theta$$</p>
<p>where $r$ is the distance between the two particles. This is the rate at which $B$ moves away from $A$ at time $t$. They then integrate the above and set it equal to $l$, which I don't understand:</p>
<p>$$\int_0^T(v - u\cos\theta)dt = l \tag3$$</p>
<p>How is this integral equal to $l$? If we consider the time when $A$ is about to meet with $B$, in a small time interval, the displacement of $A$ as given by $(3)$ would be along the line of motion of $B$ rather than perpendicular to it. How is this possible? </p>
<p><strong>EDIT</strong>: This problem is from General Problems in Physics by IE Irodov</p> | g10761 | [
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<p>I'm interested in the relation between the probability distribution $p_i$ over states of a system on the one side and the density of states $\rho(\eta)$ of its environment. (Meaning, $\int_{\eta_a}^{\eta_b} \rho(\eta) ~ \mathrm{d} \eta$ is the number of environment states with energies in the interval $[\eta_a, \eta_b]$.)</p>
<p>If the whole (system + environment) is energetically closed ("isolated") with a total energy $E = e + \eta$, but system and environment are in thermal equilibrium (i.e. the whole is described by the microcanonical ensemble), then it holds
$$
p_i = \frac{ \rho(E - e_i) }{ \sum_i \rho(E - e_i) }.
$$</p>
<p>This means, the probability distribution over states of the system is determined by a) something that only characterizes the energetic <em>structure</em> of the system (the $e_i$s), b) something that only characterizes the energetic <em>structure</em> of the environment ($\rho(\eta)$) and c) the total energy $E$.</p>
<p>This relation holds generally, for arbitrary small or large systems and/or environments. Please note that we have not yet taken any limits!</p>
<p>If we now consider the thermodynamic limit, i.e. an environment composed of an infinite number of subsystems, the probability distribution $p_i$ over states of the system becomes the Boltzmann–Gibbs-distribution (aka canonical ensemble)
$$
p_i = \frac{ \exp(- \beta e_i) }{ \sum_i \exp(- \beta e_i) }.
$$
Using the first relation above, this distribution could now be interpreted as corresponding to a <em>limiting density of states of the environment</em> of the form
$$
\rho(\eta) \propto \exp( \beta \eta )
$$
which characterizes the "infinite environment". However, the expression refers to the parameter $\beta$ of the Boltzmann–Gibbs distribution, which represents the temperature and depends on the total energy $E$ (per subsystem). Whereas in the finite case $E$ only serves to connect $\rho(\eta)$ and $p_i$, it here defines $\rho(\eta)$ itself.</p>
<p>To me this suggests that it does not make sense to characterize an infinite environment by a density of states – but maybe there's some way around this? Or is there a mistake in the derivation somewhere else?</p> | g10762 | [
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<p>I conducted an experiment which aimed to detail and record the voltage across series resistors in series circuits.</p>
<p>I noticed that:</p>
<ul>
<li>The Final Voltage, V3, stayed the same.</li>
<li>The resistors with the highest resistance had the highest voltage drop.</li>
</ul>
<p>How do I put my observation in words?</p> | g10763 | [
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<p>I have a (hopefully) quick question: is it possible to have a null Killing field $\xi ^ \mu$ such that the twist 1-form $\omega_{\mu} = \epsilon_{\mu\nu\alpha\beta}\xi^\nu \nabla^\alpha \xi^\beta \neq 0$ but the exterior derivative $(d \omega)_{\mu\nu} = 2\nabla_{[\mu}\omega_{\nu]} = 0$? Or does $(d \omega)_{\mu\nu} = 0$ always imply $\omega_{\mu} = 0$ for a null Killing field? </p> | g10764 | [
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<p>Shall we consider photoelasticity a non-mathematical, or purely visual, proof of the existence of stresses in mechanical structures undergoing external loading?</p> | g10765 | [
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<p>At a free massless Lagrangian
\begin{equation} L_0 = \frac 1 2 ( \partial \psi)^2 ,\end{equation}
add an interaction term \begin{equation} L_I = \frac 1 2 m^2 \psi^2\end{equation}
where m is small enough to converge its perturbation calculation. From these setup, is it possible to gain the same results as of the free massive Lagrangian? Please point me a book description or some internet site. Thanks.</p> | g10766 | [
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<p>Today I was doing my physics homework and there was a problem involving a space ship falling at 9.8 m/(s^2) to simulate gravity, and it asked how long would it take for the ship to reach to speed of light, and I calculated it to be just under a year. So if it takes less than a year to go to the speed of light at 9.8m/(s^2) to reach the speed of light and proximus centari is one light year away even with the consequences of relativity (which I understand in the abstract) why does it not take about six years to get to alpha centari, and why will it take Voyager (travelling at a much faster acceleration) so long, especially in space where there is no friction?</p>
<p>Thank you.</p> | g10767 | [
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0.0298... |
<p>Let me preface this by saying that I have a very limited knowledge of optics -- basically, I know enough to be dangerous. So I have a square Fresnel lens that measures about 10.5 inches on a side. The focal length is about 11.5 inches. I'm trying to find a presumably-smaller glass collimating lens that will take the light from the Fresnel lens and convert it to a beam with an indefinite focal length (or at least, a focal length of a few feet). I don't care about image preservation, I just mainly want to transfer some focused light from point A to point B with a minimum of loss. I basically need to know what kind of lens to buy and where to place it. I've tried single and double convex and concave lenses and seemed to have the most luck with single convex, but wasn't able to get much of a beam past a couple of inches out. The attached picture shows kind of what I am looking for (lens on left represents Fresnel lens, lens on right represents collimating lens).</p>
<p>Any help you could give me with this would be great. </p>
<p><img src="http://i.stack.imgur.com/fWk1M.png" alt="enter image description here"></p> | g10768 | [
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<p>At the end of spontaneous symmetry breaking I get these mass terms:</p>
<p>$$W_{\mu}^{\pm}=\frac{1}{\sqrt{2}}\bigl(W_{\mu}^{1} \mp i W_{\mu}^{2} \bigr )$$</p>
<p>$$\mathcal{L}_{mass}=\frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{+}{W^{\mu}}^{-} + \frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{-}{W^{\mu}}^{+}$$</p>
<p>So I have $$M_{W^+}=g \frac{v}{2} \quad M_{W^-}=g \frac{v}{2} $$</p>
<p>Is it right? Or there are too many terms and it is enough:</p>
<p>$$\mathcal{L}_{mass}= \frac{1}{2} g^2 \frac{v^2}{4} W_{\mu}^{-}{W^{\mu}}^{+} $$</p> | g10769 | [
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0.0... |
<p>It would really help me with an idea I have if I could see how something such as a symmetric field could collapse to something asymmetric. I know that if $x$ occures before $y$ is symmetric, then $y$ occurs before $x$, which doesn't make sense if we take time to be asymmetric (only flowing in one direction). Is there a relationship between energy in the universe being symmetric, and the production of anti-matter asymmetric? </p>
<p>I am mostly interested in the collapse of the wavefunction, and a search to find if this collapse is asymmetric I am left with the thought that I might have to specify what the symmetry/asymmetry would be in respect to, that being said, is there some sort of "field" whether physical or purely abstract which is symmetric and if a "disturbance" (observation?) happens, there is a collapse to an asymmetric field such as the collapse of the wavefunction? Maybe I have it all wrong?</p>
<ul>
<li>Digging deeper, what I am looking for examples of, especially of quantum systems is that of "symmetry breaking". I also found the answered question concerning spontaneous symmetry breaking in Quantum mechanics here: <a href="http://physics.stackexchange.com/questions/29311/what-is-spontaneous-symmetry-breaking-in-quantum-systems">spontaneous symmetry breaking in Quantum Systems</a>, and while I have some background in physics and pure math, I hope to get a much more canonical answer so as to understand more the foundations. \</li>
</ul> | g10770 | [
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0.039810627698898315,
... |
<p>Did the geocentric theorists also use the fact that the earth had an axis tilt? Or was their explanation of some other kind?</p> | g10771 | [
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0.033935654908418655,
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<p>I've been considering a career change for a long time and recently discovered the Two-Slit Experiment, which, to put it frankly, blew my mind. I then started some hefty reading and investigation into all things Quantum (Bell, Campbell, entanglement, QIT), which has led me here.</p>
<p>I have 20 years experience in IT working as a programmer, having graduated with a Bachelor in Computer Science back in the early 90s. As mentioned, I have been considering a career change for some time (having become quite burned out in this industry), and have found something that has piqued my interest more than anything else (tho I did consider Astrophysics a couple of years ago). I am not yet sure which area of "Quantum" I will be most drawn to, possibly Quantum Information Theory/Science. </p>
<p>I am aware that there is a significant amount of Maths and Physics pre-requisites involved. It seems likely, given that I have not done any Maths or Physics study probably since I was doing my CS undergrad, that I will need to start over with an undergrad in Science/Physics in order to get the fundamentals.</p>
<p>So my questions are:</p>
<ol>
<li><p>What is the ideal path of education to get to QIT/QIS or QM?</p></li>
<li><p>Is the path to QIT/QIS also via the Physics route? Can I leverage my CS background?</p></li>
<li><p>Resources (books, online courses, etc) that would help with the transition from CS-type thinking to Physics/Maths-type thinking.</p></li>
</ol>
<p>Apologies if this encompasses elements too broad or off-topic, I'm trying to get a better understanding on what is to come following this path. Thanks in advance.</p> | g10772 | [
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<p>The paramount object in generalized gomplex geometry is the Courant algebroid $TM\oplus T^\star M$, where the manifold $M$ is called <em>background geometry</em> I think (I am not sure). More generally this Courant algebroid can be twisted by a closed 3-form $H$ on $M$, which I suspect is called a <em>flux</em> (I am not sure too). In fact P. Severa shown that every exact Courant algebroid arise as such a twist of the standard Courant algebroid $TM\oplus T^\star M$. I think these objects arise in Physics when one tries to make compactifications with fluxes in String Theory, which are more realistic ones. They also appear in the AdS-/CFT correspondence (see <a href="http://physics.stackexchange.com/questions/27615/generalized-complex-geometry-and-theoretical-physics">Generalized Complex Geometry and Theoretical Physics</a>). Please correct me if I am saying something wrong.</p>
<p>Could somebody sum up the way these forms $H$ appear in Physics in mathematical terms? However my true question is the following: could somebody provide concrete examples of both manifolds $M$ and forms $H$ such that, when combined together into the twisted Courant algebroid $(TM\oplus T^\star M,H)$ they are relevant to String Theory?</p>
<p>Thank you!</p> | g10773 | [
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<p>Just what the title states.</p>
<p>Pretty much all movement on Earth is by pushing against the much greater mass of Earth. Given there are easily thousands of aircraft taking flight/landing, and a lesser number of rockets (Satellite launch etc). Understandably the effect of aircraft would be reduced because an aircraft (usually) comes to ground eventually but with a reduced mass by virtue of the reduced fuel mass ... </p>
<p>How much is Earth's orbit affected by such reaction if observed/calculated over an extended period - say, of the order of millenia or longer? </p> | g10774 | [
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<p>I am trying to understand why radio waves pass though the human body, light does not, but X-rays still pass. </p>
<p>In my mind I imagine that radio waves don't supply enough energy and don't excite any interesting modes of the material that they hit. This is in contrast to the photon excitation and associated scattering I imagine when a light beam hits a material. </p>
<p>I am confused as to why this doesn't happen for X-rays? I mean they come out the other end, so I assume that they have a pretty good transmission though soft tissue. </p>
<p>Certainly, the 1MeV is a enough to excite the band-gaps in the human body which, in turn, should cause all the X-rays to be absorbed?</p> | g10775 | [
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<p>If I understand correctly, according to Einstein's General Theory of Relativity, mass results in a distortion in space-time. In turn, the motion of the mass is affected by the distortion. A result of the interplay between mass and space-time is that the 'force' of gravity may be explained away. Masses are not subject to a force, but are merely following a 4-dimensional space-time geodesic; gravity is just geometry.</p>
<p>And yet physicists are searching for exchange particles for the force of gravity, and are trying to unify quantum mechanics with relativity, or to unify the weak/strong/electromagnetic forces with that of gravity.</p>
<ol>
<li><p>What have I missed? Are these different communities of physicists? Does relativity explain only part of the story of masses acting under gravity?</p></li>
<li><p>Is gravity a force or not? Is it only an apparent force or not?</p></li>
<li><p>Can such an apparent force 'generate' exchange particles? Are the exchange particle and geometric models both different views of the same underlying truth?</p></li>
<li><p>A side question might be: why can't the other forces be explained away similarly? Or is that what is happening with all this talk of small extra dimensions?</p></li>
</ol>
<p>I'd appreciate any illumination on this matter, or suggested reading (preferably at the 'popular science' or undergraduate level).</p> | g10776 | [
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<p>Can someone summarize, with references if possible, all of the alternatives to the simplest model (that requires only a single scalar Higgs field with the Mexican Hat potential) of spontaneous electroweak symmetry breaking?</p> | g10777 | [
-0.01228811964392662,
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0.0721... |
<p>What impulse should be applied to an object of mass m, having a known coefficient of friction u to get to a distance d ?</p>
<p>Thanks!</p>
<p>Update 14.02.2011: </p>
<p>I still wasn't able to find an answer to this. Could you please share the solution? I need an "Idiot's solution" for this. I'm not experienced enough to find a formula by myself starting from your clues. I've searched the forums but they take into account other parameters. Thank you !</p>
<p>Update 13.02.2011: </p>
<p>Here is a representation of what I need: <img src="http://i.stack.imgur.com/Pc7qa.png" alt="http://img412.imageshack.us/img412/2192/20110213112259.png"></p>
<p>It's been a long time since I studied the principles of physics, sorry if I did not make myself clear in the first post. </p>
<p>I've tried formulas like:</p>
<p>1)m * a = u * m * g => a = u * g</p>
<p>2)a = v / t</p>
<p>3)d = v * t</p>
<p>So from these three equations, distance = u * g * t^2</p>
<p>The impulse p = m*v , so I get p= m * u * g * t</p>
<p>However, the time is not known and it is not important how long it takes for the object to get to target.</p>
<p>Does this formula (p= m * u * g * t) seem right? The mass, u, g are known, but what about time?</p> | g10778 | [
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... |
<p>Stephen Wolfram in his book <em>A New Kind of Science</em> touches on a model of space itself based on automata theory. That it, he makes some suggestions about modelling not only the behaviour of matter through space, but the space itself in terms of state machines (a notion from computing). Here, the <a href="http://en.wikipedia.org/wiki/General_topology" rel="nofollow">general topology</a> of space arises from a small-scale connection lattice. </p>
<p>I wondered whether any theoretical work is being undertaken along these lines within the physics community.</p>
<p>The reason for my interest in this regards one of the mysteries of quantum mechanics, that of quantum entanglement and action at distance. I wondered whether, if space is imagined as having a topology that arises from a notion of neighbourhood at a fine level, then quantum entanglement might be a result of a 'short circuit' in the connection lattice. That is two points at a distance through 'normal' space might also still be neighbours at a fundamental level; there might be a short strand of connectivity in addition the all the long strands relating the two.</p>
<p>(I think Richard Feynman also alluded to this sort of model with his take on quantum electro-dynamics.)</p> | g10779 | [
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<p>or a phenomenon where we can only measure the standard deviation ($\sigma_w$) of a variable $w$ and not the mean $\overline{w}$</p> | g10780 | [
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... |
<p>Is there a certain frequency of sound/noise that will cause gunpowder to explode?</p> | g10781 | [
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<p>I’ve been studying electricity lately and it has been quite hard to understand the terminology, and picturing it in my mind. After struggling to understand what each property of electric currents meant, I found an analogy that related electric current to water flow. I am not sure if this analogy is 100% accurate, but it sure has helped me understand the complex (at least for young, starter scientist like me) topic of electricity. This far I have managed to relate in the analogy that:</p>
<p>-----Electricity-------------------------Water------------</p>
<p>Current (Amps)(A)-------Flow rate (Volume/Time)</p>
<p>Resistance (Ohms)(Ω)----pipe size (Inches)</p>
<p>Voltage (Volts)(V)------Water pressure (psi)</p>
<p>But I am still missing properties like charge. What properties am I missing? How could it be related to water flow? If it can’t be related, can you please give me a short definition and explanation to better grasp the concept? Please include units in both sides of the analogy. Also, please keep the answer short and simple for us, the inexpert scientist (including me) that struggle to grasp the concept.</p>
<p><strong>Thanks a bunch for your expert help</strong></p>
<p>It is kind of discussed in these articles:</p>
<p><a href="http://physics.stackexchange.com/questions/10373/flow-of-water-and-flow-of-electrons-how-this-analogy-works">Flow of water and flow of electrons, how this analogy works?</a></p>
<p><a href="http://physics.stackexchange.com/questions/66629/power-in-hydraulic-analogy">Power in hydraulic analogy</a></p>
<p>But I couldn’t find (or understand) the answer provided in them.</p> | g10782 | [
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<p>Almost every source I can find online maintains that two 0.5 cm blankets are significantly warmer than a single 1cm blanket due to air trapped between the thin blankets.</p>
<p>However, the thermal conductivities of air and wool are roughly comparable according to <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/tables/thrcn.html">this website</a>. That would seem to mean that air only aids the insulation significantly if the thickness of the air layer is significant compared to the thickness of the blankets, which I would guess it is not.</p>
<p>Further, in order for heat transfer through the air to be dominated by conduction, the air needs to be extremely still, which it seems it would not be around a living, breathing, human. Otherwise the air would mix and not provide significant insulation.</p>
<p>Is there any empirical evidence that two thin blankets are superior? If so, why is that, given the above considerations?</p> | g10783 | [
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<p>The resultant force acting on a body in equilibrium is 0:</p>
<p>$$\iiint_R \rho {\bf b}\ dV + \iint_S {\bf t}^{(n)} ds = 0,$$</p>
<p>in which $R$ is a region inside the body, $\rho {\bf b}$ the body force per unit volume, $S$ the surface of the region and ${\bf t}^{(n)}$ the surface traction.</p>
<p>I am not quite sure what to make of all these parts... for example, let $R$ be a solid cube made from uniform material, resting on a table. In this case $S$ consists of the 6 faces of the cube, and $\rho$ is its (constant) density. </p>
<p>But what are ${\bf t}^{(n)}$ and $\bf b$?</p>
<p>It seems ${\bf t}^{(n)}$ should point upwards (against gravity) on every point on the bottom face of the cube, and be 0 on the other five faces. Also, I think $\bf b$ is the gravitational acceleration $g$... is this correct?</p> | g10784 | [
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<p>I was concerned about what determines the speed of the bullet coming out from the gun.</p>
<p>Is it determined by the strength of the explosive or how fast does it burn up?</p>
<p>For example if we take the same amount of gun powder and a plastic explosive (probably TNT) in a bullet shell which bullet will go further the one with the plastic explosive or the one with the gun powder</p> | g10785 | [
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<p>Consider a parallel-plate capacitor. Charge is stored physically on electrodes ("plates") which are flat and parallel to one another. If one electrode has charge $+Q$ and the other electrode has charge $-Q$, and $V$ is the potential difference between the electrodes, then the capacitance $C$ is $$C = \frac{Q}{V}$$</p>
<p>(This definition of $C$ is given in, for example, <em>Introduction to Electrodynamics</em> by David J. Griffiths.)</p>
<p>But, now, let's think about the energy stored in the electric field between the electrodes of this parallel-plate capacitor. As stated in Griffiths on page 105, "How much work $W$ does it take to charge the capacitor up to a final amount $Q$?" It turns out that $W$ is $$W = \frac{1}{2} CV^2$$</p>
<p>So:</p>
<p>(i) the capacitor's capacitance $C$ goes like $\frac{1}{V}$; and </p>
<p>(ii) the energy $W$ stored in the electric field goes like $V^2$. </p>
<p><strong>Are statements (i) and (ii) at odds with one another?</strong> I am sure that they <em>cannot</em> be. But conceptually I am having difficulty.</p>
<p>We desire high capacitance -- we want to put as much charge on the electrodes as possible, because if we accomplish this, then I think that will increase the energy density of the system. But is what I just said true?</p>
<p>If we manage to increase $Q$, then by $V = \frac{Q}{C}$, the potential difference $V$ between the plates will also increase. This, I think, is why capacitor electrodes are separated by a material (such as a polarizable dielectric material like a slab of plastic); otherwise $V$ will become too large and the breakdown voltage will be reached, generating a spark.</p>
<p>But, now, the equation $W = \frac{1}{2} CV^2$ (where I think that $W$ can be conceptualized as the energy stored in the electric field between the electrodes) seems to say that as $V$ increases, so does the energy $W$, quadratically.</p>
<p>So, my question is, <strong>do we want a capacitor to have a <em>large</em> potential difference $V$ or a <em>small</em> potential difference $V$?</strong> If $V$ is large, then $W$ is large (which we want), but $C$ is small (which we do <strong><em>not</em></strong> want).</p>
<p>Am I somehow thinking of two different potential differences $V$ and confusing them?</p> | g10786 | [
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<p>I would like to know how to take the functional derivative of the holonomy, or Wilson line. I have tried it and I will show what I have done below, but before I wanted to say that I also have seen and done this with the characteristic deifferential equation for the holonomy
$$
\frac{\partial U}{\partial s}+\dot{\gamma}^a A_{a} U=0
$$
with $\dot{\gamma}$ a tangent vector to the curve and $A$ the connection. By varying this equation I can find what $\frac{\delta U}{\delta A}$ is, but I would like to know how to do it from the expression for $U$
$$
U=\mathcal{P}\exp \left[ -\int_{\gamma} \dot{\gamma}^a(s) A_a(\gamma(s)) ds \right]
$$
with $\dot{\gamma}^a=\frac{dx^a}{ds}$ as before. Now I have tried to directly vary this with respect to $A_b$
$$
\frac{\delta U}{\delta A_b(x)}=\mathcal{P} \exp \left[ -\int_{\gamma} \dot{\gamma}^a A_a ds \right] \cdot \frac{\delta}{\delta A_b}\left[ -\int_{\gamma} \dot{\gamma}^a A_a ds \right]
$$
Now if $A_a=A_{a}^{i}\tau^i$ then
$$
\frac{\delta}{\delta A_{b}^i }\left[ -\int_{\gamma} \dot{\gamma}^a A_{a}^j \tau^j ds \right]=-\int_{\gamma} \dot{\gamma}^a \delta _{ab}\delta_{ij} \delta^3(\gamma(s)-x) \tau^j ds=-\int_{\gamma}\dot{\gamma}^b \delta^3(\gamma(s)-x) \tau^j ds
$$
So I end with
$$
\frac{\delta U}{\delta A_{b}^j}=U(\gamma)\left[ -\int_{\gamma}\dot{\gamma}^b \delta^3(\gamma(s)-x) \tau^j ds \right]
$$
Which isn't right.. Can someone point me in a better direction, Thanks.</p> | g10787 | [
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<p>I always get a little uneasy that all the theories I can think of (at least since Newton) are constructed in a way such that they would be true in heaven and on earth ... but we can never go everywhere and test it out. </p>
<p>So here is the question:</p>
<blockquote>
<p>Is there some good justification to implement something like the principle of relativity in scientific theories other than it turned out to work good so far? </p>
</blockquote>
<p>Some more motivation:</p>
<p>We have an understanding of different places in space (and time) and what different velocities are. Like imagine me and my droogs cruising our skateboards down the neighborhood and there is a truck driving in the other direction. I see a cactus on the roadside and I wonder how the trucker in his ride sees it. </p>
<p><img src="http://i.imgur.com/7qhvM.png" alt=""></p>
<p>Now in the maths, space $\vec x$ and spacetime $t$ represent physical space and physical time. And if I know my coordinates, the form of the plant and its location and orientation in space, I can find out what I see and also what the trucker from his position sees. A <em>coordinate transformation</em> (replacing some letter on a piece of paper with some other letters in a systematic way) is conventually interpreted as taking the data from one "perspective" and transforming it into "another perspecitive".</p>
<p>It's supposed to be a fruitful approach to physics to consider only the observable quantities. Maybe I interpret the principle of relativity the wrong way, but I find it funny that a theory tells me there are spacetime events where I can never get to (outside the light cone). And simultaneously I'm guaranteed that if I'm there I would also be able to physics and come to the right conclusions. At the very least, I feel this is somewhat redundant - why not drop it?</p> | g10788 | [
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<p>I was reviewing the paper-<a href="http://www.sciencedirect.com/science/article/pii/S0370269304010032" rel="nofollow">Coupling of a vector gauge field to a massive tensor field</a></p>
<p>In the calculation I found the term $ 2\mu^2 \varepsilon^{ijk} \dfrac{\partial_j}{\partial^2}B_k\dot{B}$ which needed to be integrated by parts. How can I do this? Please help me.</p>
<p><em>Note</em>: Here $B_k$ is the space component of an antisymmetric tensor field and $\dot{B}$ is the time derivative of $B_k$.</p>
<p>(<em>Edit: corrected the index</em>)</p> | g10789 | [
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<p>are bubbles of spacetime pinching-off allowed solutions to general relativity? With "pinch-off bubble" i really mean a finite 3D volume of space whose 2D boundary decreases until it reaches zero and it disconnects from the mother spacetime, becoming a compact "child" spacetime</p>
<p>I've read this as a way in eternal cosmologies to produce new universes, but i don't know if that is something something allowed in general relativity or is something from a more advanced theory (i.e: string theory) </p>
<p>In particular, unlike unitary black holes, this does not seem to conserve information, unless someone believes that complementarity can do strange things as clone the information (including the quantum one). Does that automatically make this an unphysical solution?</p> | g10790 | [
-0.03958120197057724,
0.044583287090063095,
0.02074040099978447,
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0.0011690607061609626,
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0.018936924636363983,
0.029831495136022568,
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0.04428066313266754,
0.0... |
<p>Internal resistance of inductance (or other devices) are said to be in series. But <a href="http://en.wikipedia.org/wiki/Parasitic_capacitance" rel="nofollow">parasitic capacitance</a> is said to be in parallel (in case of an inductor). Why is that so? What determines whether an internal property is in series or parallel?</p> | g10791 | [
0.022146614268422127,
0.05272882059216499,
-0.010624692775309086,
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0.023183515295386314,
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0.003810230176895857,
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-0.... |
<p>I recently came across <a href="http://link.springer.com/article/10.1140%2Fepja%2Fi2013-13072-1" rel="nofollow">this article</a>, published in the respectable <em>European Physical Journal A</em>. (Apparently, there isn't any corresponding arXiv article for this, so I'm sorry if everyone isn't able to access the article.)</p>
<p>Here's the possibility that the author has suggested:</p>
<blockquote>
<p>While looking for the putative Higgs boson of the Standard Model of particle physics, recently, the CMS and the ATLAS experiments at CERN have found strong signals of a new particle at about 125 GeV. ... </p>
<p>Here we show that what they may have found at 125 GeV is the long sought for and missing ingredient of the strong interaction: the sigma-meson of the Chiral Sigma Model, within the framework of the Skyrme model with a topological interpretation of the baryons. Just like a massless gauge boson is a requirement, and hence a prediction of the local gauge theories, in the the same manner, a very heavy scalar meson is a requirement and hence a prediction of the Skyrme model of the hadrons. The 125 GeV particle discovered by the CMS and the ATLAS groups may be an experimental confirmation of this unique prediction of the topological Skyrme model. However the bottom line is that even if the experimentalists finally confirm that this 125 GeV entity is the expected Higgs boson, then there still remains to discover another heavier scalar particle as the sigma-meson of the chiral sigma model/Skyrme model, which remains its unique prediction, as shown in this paper.</p>
</blockquote>
<p>I appreciate that the physics community in general must be very confident that they have identified Higgs correctly (they wouldn't have awarded a Nobel prize if there was any doubt remaining).</p>
<p>The point is, while hoaxes keep sprouting up all the time, this is a well-sourced and peer-reviewed article. Does this possibility appear irrational for any definite reason? Especially since this $\sigma$ meson is still elusive? </p>
<p>Edit : Found another. This one is in Phys. Rev. D and incidentally carries the same name as my question title ! Here are the links - <a href="http://journals.aps.org/prd/abstract/10.1103/PhysRevD.86.093012" rel="nofollow">PRD Link</a>, <a href="http://arxiv.org/abs/1207.1093" rel="nofollow">arxiv link</a> </p> | g10792 | [
0.023818830028176308,
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0.032083891332149506,
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0.06452883034944534,
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0.014135426841676235,
0.0025362581945955753,
-0.012608322314918041,
... |
<p>I am trying to wrap my head around how this would work.</p>
<p>The setup is quite simple - there are multiple flat coils sealed in insulated disks, and an active coil with alternating current underneath. All is placed in a cylinder.</p>
<p>The question is, how will the disks behave - all should induce the same magnetic field and thus repel each other. Will this force be stable enough, when the field collapses on each pulse?</p>
<p>Thanks!</p> | g10793 | [
0.003027467057108879,
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0.026323264464735985,
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-0.05186820775270462... |
<p>I am trying to locate peak in a data set by numerically calculating the peak using <a href="http://mathworld.wolfram.com/FunctionCentroid.html" rel="nofollow">centroid method</a>. How can I estimate the error associated with this peak determination?</p> | g10794 | [
0.040094513446092606,
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0.017173049971461296,
0.019746607169508934,
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0.007815485820174217,
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0.04688921570777893,
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0.... |
<p>I have a system of particles with equal distance with each other and another at random positions which is moving with time. What I want to know is :</p>
<ol>
<li><p>The method by which I can reduce the number of particles from the first system, as I know the maximum motion of any particle is X (<strong>Meaning: Maximum displacement from starting to end of simulation is X)</strong>.</p></li>
<li><p>How to efficiently calculate the collision between them, I have heard about quadtree and octree but (as per I understood till now) they are for collision of particle from each other. In my problem,second system of particles doesn't collide with each other.</p></li>
</ol>
<p>Note: Sorry, if it is a very basic question, I am (very) new to this field.</p>
<p><strong>Update:</strong></p>
<p><img src="http://i.stack.imgur.com/ZTixa.png" alt="enter image description here"></p>
<h2><strong>The combined System</strong></h2>
<p><img src="http://i.stack.imgur.com/uEgwX.png" alt="enter image description here"></p>
<h2><strong>Movable parts (Same color means same radius and mass)</strong></h2>
<p><img src="http://i.stack.imgur.com/i3whf.png" alt="enter image description here"></p>
<h2><strong>Unmovable Grid (Colors means nothing and yes, it's a cube of spheres)</strong></h2> | g10795 | [
0.04263673722743988,
0.034893669188022614,
0.01346308458596468,
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0.038539133965969086,
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0.006556562148034573,
0.06099054589867592,
-0.01... |
<p>I'm just curious what causes radioactivity. I've been told that in the case of alpha decay, since the nucleus is quantum mechanical, there is a probability that the configuration of protons and neutrons is in such a way as to have an alpha particle outside the nucleus, and then the electric repulsion pushes it away. Is this true? Does quantum mechanics give a probability of this sort of thing happening which would be connected to the half life. Also the second part of my question is,why we don't have many other kinds of decay, why alpha particles or beta only (and fission etc artificially)? Thanks a lot in advance, if you can point to articles or books I can read on the subject it would also be a plus.</p>
<p>edit: for the configuration , I mean some kind of quantum entanglement or uncertainty principle.</p> | g10796 | [
0.04196641594171524,
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0.00571186188608408,
0.003167241346091032,
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0.017121... |
<p>I would like to know the following:</p>
<ol>
<li><p>What is the angle at which water gets splashed when I ride my vehicle through a water on the road?</p></li>
<li><p>How does angle of water varies with speed?</p></li>
<li><p>What is the relation between the distance the water goes with the speed of the vehicle?</p></li>
</ol>
<p>Thanks!</p> | g10797 | [
0.003968472592532635,
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0.03362959250807762,
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0.028669720515608788,
0.035024553537368774,
0.0... |
<p>I know the hypothesis that the light speed is constant is retained by experiments. But is there any theory explaining why the light speed is constant no matter how an observer moves relative to light?</p>
<p>My question is, specifically: Suppose an observer $O$ launches a light and $O$ starts to move at the same time with a uniform velocity $v$ in the same direction that light points. Then why $c$ is still the light speed that $O$ will measure rather than $c-v$? </p> | g348 | [
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0.00496953260153532,
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0.018977070227265358,
0.007556945085525513,
0.014438151381909847,
0.0... |
<p>Given the lowest eigenvalue $E_0$ of an Schrödinguer operator, do the other energies $ E_{n} $ for $ n >0 $ depend strongly on the lowest eigenvalue of the system? I mean, if we somehow fixed the eigenvalue $E_{0}$, could we get more or at least better approximations to the other eigenenergies of the system?</p>
<p>thanks</p> | g10798 | [
0.03219647705554962,
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0.011015159077942371,
0... |
<p>It is postulated by many cosmologists that at the Big Bang time the universe was in an unusual low entropy state.</p>
<p>Does this claim specifically mean that the entropy of the initial universe was zero?</p>
<p>Is zero-entropy state unique for given physical laws?</p>
<p>Is it possible that entropy was growing always so that only difference in entropy has physical meaning rather than absolute value? Was there ever negative entropy state?</p> | g10799 | [
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0.005402720998972654,
0.021185003221035004,
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0.010554611682891846,
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0.012986497953534126,
... |
<p>Let's have minimally extended gauge invariant lagrangian (with free kinetic term of EM field):
$$
\tag 1 L (\Psi , \partial_{\mu} \Psi) \to L (\Psi , D_{\mu}\Psi ) - \frac{1}{4}F^{\mu \nu}F_{\mu \nu}, \quad D_{\mu} = \partial_{\mu} - iQA_{\mu}.
$$
Here $A_{\mu}$ is given by $F_{\mu \nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}$ .</p>
<p>It is well-known result that for an arbitrary amplitude of EM process (I have cut here photon propagators and polarization vectors; all of operators here is given in Heisenberg picture)
$$
\tag 2 M^{\mu_{1}...\mu_{n}}(q_{1}, ..., q_{n}) = \int d^{4}x_{1}...d^{4}x_{n}e^{iq_{1}x_{1} + ...+iq_{n}x_{n}} \langle | \hat{T}\left( \hat{J}^{\mu_{1}}(x_{1})...\hat{J}^{\mu_{n}}(x_{n}) \right)|\rangle ,
$$
$$
\hat{J}^{\mu} = \hat{\bar{\Psi}}\gamma^{\mu}\hat{\Psi}, \quad \partial_{\mu}\hat{J}^{\mu} = 0,
$$
we have identity
$$
\tag 3 q_{\mu_{i}}M^{...\mu_{i}...} = 0.
$$
Let's have than non-zero photon mass. Then we will get modified photon propagators (so the new force law) and non-invariance of lagrangian, but $\hat{J}_{\mu}$ is still conserved, so it seems that $(2)$ still satisfies identity $(3)$. I have checked this statement for processes $WW^{+} \to \gamma \gamma$ and $e e^{+} \to \gamma \gamma$ at the lowest order.</p>
<p>But is this statement true in general? If yes, why we usually say that photon must have strictly zero mass (nonzero but very small mass doesn't contradict the experimental data)? I'm not interested in Higgs mechanism, because I'm not interested in exactly gauge invariance.</p> | g10800 | [
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0.03553725406527519,
-0.00942769180983305,
-0.029267551377415657,
0.02... |
<p>In Peskin and Schroeder p. 669 it is argued that the axial current can be parametrized between the vacuum and an on-shell pion state as:</p>
<p>$$<0|j^{\mu 5}(x)|\pi^b(p)>=-ip^\mu f_\pi \delta^{ab}e^{-ipx}$$</p>
<p>This is then described as a parametrization of the amplitude for the axial current to create a pion state from the vacuum. This interpretation puzzles me: isn't it the role of the creation operators of a given theory to do this? Does the above expression correspond to an actual physical process or is it just part of an amplitude in a Feynman diagram for an actual process?</p> | g10801 | [
0.03919638320803642,
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0.08137673884630203,
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0.008694385178387165,
-0.04936814308166504,
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0.01556445937603712,
0.015... |
<p>I am trying to understand what a term like $$ \mathcal{L}_{int} = (\partial^{\mu}A )^2 B^2 $$ with $A$ and $B$ being scalar fields for instance means. I understand how to draw an interaction term in Feynman diagrams without the derivative and how to interpret it (connecting external lines, find the correct value for the interaction coupling constant and so on).</p>
<p>But if I have a derivative in front of one of the fields, how do I interpret it ? Is it still two $A$ scalar particles interacting with two $B$ scalar particles ? How the derivative changes the interaction ?</p>
<p>I search a bit on Internet about that and found some resources : <a href="http://www.theory.caltech.edu/~preskill/ph205/205Chapter4-Page1-63.pdf">Preskill Notes</a> (see p. 4.33) or <a href="http://www.maths.tcd.ie/~cblair/notes/list.pdf">Useful Formulae and Feynman Rules</a> (see p. 20) but still... Don't understand. </p> | g10802 | [
0.05710527300834656,
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0.04012233763933182,
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0.04928957670927048,
0.01058705523610115,
-0.... |
<p>I am learning about waves (intro course) and as I was studying Wave Functions, I got a little confused.</p>
<p>The book claims that the wave function of a sinusoidal wave moving in the $+x$ direction is $y(x,t) = A\cos(kx - wt)$.</p>
<p>However, I see a drawing of the wave and they always seem to be $\cos$ graphs. Are sinusoidal waves always cosine graphs? Or can they be sine? If I ever see a sine wave, then does that mean that this is merely a pulse/wave travelling once and not oscillating in a periodic motion?</p>
<p>Sorry for the basic beginners question.</p> | g10803 | [
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0.03710733354091644,
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0.008103277534246445,
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0.018798936158418655,
-0.0468280166387558,
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0.0637708306312561,
0.03662321716547012,
0.022... |
<p>I'm convinced that radians are, at the very least, the most convenient unit for angles in mathematics and physics. In addition to this I <em>suspect</em> that they are the most fundamentally natural unit for angles. What I want to know is why this is so (or why not).</p>
<p>I understand that using radians is useful in calculus involving trigonometric functions because there are no messy factors like $\pi/180$. I also understand that this is because $\sin(x) / x \rightarrow 1$ as $x \rightarrow 0$ when $x$ is in radians. But why does this mean radians are fundamentally more natural? What is mathematically wrong with these messy factors?</p>
<p>So maybe it's nice and clean to pick a unit which makes $\frac{d}{dx} \sin x = \cos x$. But why not choose to swap it around, by putting the 'nice and clean' bit at the unit of angle measurement itself? Why not define 1 Angle as a full turn, then measure angles as a fraction of this full turn (in a similar way to measuring velocities as a fraction of the speed of light $c = 1$). Sure, you would have messy factors of $2 \pi$ in calculus but what's wrong with this mathematically?</p>
<p>I think part of what I'm looking for is an explanation why the radius is the most important part of a circle. Could you not define another angle unit in a similar way to the radian, but with using the diameter instead of the radius?</p>
<p>Also, if radians are the fundamentally natural unit, does this mean that not only $\pi \,\textrm{rad} = 180 ^\circ$, but also $\pi = 180 ^\circ$, that is $1\,\textrm{rad}=1$?</p> | g10804 | [
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0.05131428688764572,
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0.07826647907495499,
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0.0479792021214962,
0.016772298142313957,
-0.0... |
<p>I know it's not possible with Earth today, but With today's level of material science technology, would it be possible to make cable strong and light enough to make a space elevator system connecting a Mars-synchronous satellite to an anchor on Mars' surface, ignoring any load at all by an elevator car? Or can someone say with a high degree of certainty that the level of strength to weight possible in cables today is still far from possible even with Mars' lower mass compared to Earth?</p> | g10805 | [
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0.05167117342352867,
0.004116690251976252,
0.016453659161925316,
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... |
<p>I am wondering if someone could provide me with a formula that would tell me at what velocity a projectile can be launched from something using an electromagnetic field. The idea is much like a rail gun or Gauss rifle, but not exactly.</p>
<p>Just looking to find a formula to determine the speed of the projectile.</p>
<p>Thank you,
Michael Vanderpool</p> | g10806 | [
0.03000030666589737,
0.012733065523207188,
0.017004486173391342,
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0.06806989014148712,
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0.025334032252430916,
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0.05692228674888611,
0.03856098651885986,
0.01135... |
<p>When we pierce a balloon with a sharp needle, it pops and produce a great sound. But, It doesn't pop when we open the mouth of the balloon (through which we have blown air)...</p>
<p>So, Why doesn't the gas release slowly when we pierce it with a needle. In fact, it is released slowly when we release the mouth. </p> | g10807 | [
0.03201143443584442,
0.01760602742433548,
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0.03560417890548706,
0.015264215879142284,
0.015670668333768845,
0.0260... |
<p>I have an electron moving with speed $u'$ in a frame $S'$ moving with speed $v'$ relative to a rest frame $S$.</p>
<p>How do I find the total energy and momentum of the electron in the rest frame $S$?</p>
<p>I thought the equations were:</p>
<p>$E_{total} = \gamma \times mc^2$<br>
$p = \gamma \times mv$</p>
<p>But, that doesn't look right... Could someone point out to me what is wrong here?</p> | g10808 | [
0.04765022546052933,
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<p>Is the S-matrix the only observable in string theory? What about time varying spacetime backgrounds, or thermal states then?</p> | g10809 | [
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<p>A theoretical question which thought about instead of writing my C++ code. I know it is poorly defined however I am now intrigued as to the answer!</p>
<p>If you got into a boat in the middle of the sea before sunrise, and as the sun cam up sailed directly towards it, and continued to do so throughout the day until you were heading west in the evening at sunset, and then stopped at sun down. Repeat this for say a week/month, then look on a GPS device as to the path you have traveled, what shape would your path/footprint be?</p>
<p>Everyone I have asked has come up with a different answer, and short of buying a boat not sure how to work it out.</p> | g10810 | [
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0.09093313664197922,
0.... |
<p>Norton's dome is the curve $$h(r) = -\frac{2}{3g} r ^{3/2}.$$ Where $h$ is the height and $r$ is radial arc distance along the dome. The top of the dome is at $h = 0$. </p>
<p><img src="http://i.stack.imgur.com/t7JI7.gif" alt=" "></p>
<p><em>Via <a href="http://www.pitt.edu/~jdnorton/Goodies/Dome/index.html">Norton's web.</a></em></p>
<p>If we put a point mass on top of the dome and let it slide down from the force of gravity (assume no friction, mass won't slide off dome), then we will get the equation of motion $$\frac{d^2r}{dt^2} ~=~ r^{1/2}$$ (Not just me, lots of sources give this answer).</p>
<p>But this equation of motion doesn't make sense. Because as $r$ becomes large, the tangential force is also becoming large. The tangential force should always be less than or equal to the drive force from gravity. What am I seeing wrong? </p> | g10811 | [
0.05943530797958374,
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0.027696434408426285,
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-0.04366210848093033,
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-0.006609862670302391,
0.045767080038785934,
-0.... |
<p>Proca action/equation describes massive spin-1 particle, but I was unable to find an equation that describes massless spin-1 particle. </p>
<p>Can anyone tell me what the name of this equation is?</p> | g10812 | [
-0.013296544551849365,
-0.03587350249290466,
0.024214137345552444,
0.04242368042469025,
0.03830365091562271,
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0.06581304222345352,
0.011385595425963402,
0.005710794124752283,
0.008025025948882103,
0.05652493238449097,
0.058737996965646744,
-0.0376... |
<p>Let a person of mass ( m ) = 10kg. then his weight will be 98N. Now, when he jumps from 1m height on the ground, the impact force becomes 9800N ( considering deflection of ground after impact is 1cm ). 100 times. But i am highly confused. 100 times force should simply crush a human! how the force is neutralized?</p>
<p>for calculating impact force:
<a href="http://hyperphysics.phy-astr.gsu.edu/hbase/flobi.html" rel="nofollow">http://hyperphysics.phy-astr.gsu.edu/hbase/flobi.html</a></p> | g10813 | [
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0.0589822418987751,
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0.055486612021923065,
0.06351811438798904,
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-0.047315116971731186,
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-0.02967211790382862,
-0.0506... |
<p>What is the <a href="http://en.wikipedia.org/wiki/Pseudotensor" rel="nofollow">pseudo tensor</a> in relativity?
How do we transform tensor and pseudo tensor under parity?</p> | g10814 | [
0.016245927661657333,
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0.04990147054195404,
-0.084... |
<p>Suppose I have an empty room of $24 m^3$ and I want to heat it to 50 °C, assuming the current room is well isolated and the current temperature is 20 °C. </p>
<ul>
<li>How much power (in Watts) would a single heating element need to produce in order to reach the 50°C? </li>
</ul>
<p>Having googled around I found this <a href="http://www.deltat.com/pdf/Quick%20estimates%20for%20wattage%20requirements.pdf" rel="nofollow">chart</a>, specifically figure 34T seems to be of interest.</p>
<p>I was looking at a heating element that provides $3 kW$ and an air displacement of $127 f^3/m$. If I'm reading the figure correctly it specifies for increases of 50 degrees. But I assume more factors are of importance, specifically the room size.</p>
<blockquote>
<p>Note:
Initially I asked this question on the general chat channel because I thought
it would be too localised and simple but It was not deemed so.</p>
<p>Edit #1: Removed the time needed subquestion, instead assume the heating element is powered on for a period of one hour time.</p>
</blockquote> | g10815 | [
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0.06375394016504288,
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0.019214268773794174,
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0.08033760637044907,
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0.03... |
<p>we know that for a one component system</p>
<p>$$U= TS - PV + N \mu$$</p>
<p>Now all terms on the right hand side have well defined zeros, but the internal energy is known to be a relative quantity, with no unique zero. What's going on?</p>
<p>Similarly, we derive the above from the fact that:</p>
<p>$$U(kS, kV, kN)= kU(S,V,N)$$</p>
<p>And it seems to me that taking $k=0$ gives us $U(0,0,0)=0$ - the internal energy of an empty system is the uniquely defined zero of energy.</p> | g10816 | [
-0.008069909177720547,
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0.0015015002572908998,
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0.06312625110149384,
-0.028427233919501305,
... |
<blockquote>
<p>A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular acceleration of the rod at the instant it is released?</p>
</blockquote>
<p>I just used </p>
<p>$$sin(30) = \frac{9.8}{a_{centripetal}}$$</p>
<p>Then I related</p>
<p>$$a_{rad} = a_{centripetal}$$</p>
<p>Is this right? I am looking at University Physics: </p>
<p>$$a_{rad} = v^2 / r$$</p>
<p>Where 9.8 is gravity. But I got none of the answers in the multiple choice ... so I must be doing wrong. Also I haven't used the radius. Any suggestions would be helpful...</p> | g10817 | [
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0.02750614657998085,
0.0008999032434076071,
0.05710630863904953,
-0.016142765060067177,
-0.0242... |
<p>A BWR reactor core may contain up to 146 tons of uranium. Why does it not form a critical mass when molten? Are there any estimates of the critical mass of the resulting zirconium alloy, steel, concrete and uranium oxide mixture?</p> | g10818 | [
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0.04310731217265129,
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0.0009... |
<p>The reply to a question about <a href="http://physics.stackexchange.com/questions/7131/origin-of-elements-heavier-than-iron-fe">nucleosynthesis</a>, that heavier than iron elements are produced in supernovae explosions, raised for me the following question which I could not answer by googling. Partially because the search for planets and stars brings out astrology answers!</p>
<p>Explosions are dispersive, nevertheless we find minerals in clumps, not only uniformly dispersed in the ground. Is there a coherent presentation that explains how minerals end up in veins and bands?</p> | g10819 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/6400/are-tidal-power-plants-slowing-down-earths-rotation">Are tidal power plants slowing down Earth's rotation?</a> </p>
</blockquote>
<p>Since we have various energy acquiring facilities that harvest energy from earth rotation. (e.g. wind, tidal power planet)</p>
<p>Will our earth rotation be slower down? Is there any form of force to accelerate earth rotation speed? </p> | g349 | [
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<p>I don't really know anything about physics even though I pretended studying it for years.</p>
<p>How is this explained?: <a href="http://andrewsullivan.theatlantic.com/the_daily_dish/2011/01/if-you-think-youre-cold-.html" rel="nofollow">http://andrewsullivan.theatlantic.com/the_daily_dish/2011/01/if-you-think-youre-cold-.html</a></p>
<p><img src="http://i.stack.imgur.com/wAlNJ.png" alt="enter image description here"></p>
<p>What is there to be said about it?</p>
<p>My apologies if you find the question too vague or silly.</p> | g10820 | [
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0.021702425554394722,
0.00... |
<p>I was reading an article in this months issue of Physics World magazine on the three main theories of extra dimensions and stumbled across something I didn't quite understand when the author began talking about detecting particles in extra dimensions at a particle lab, such as the LHC in Geneva, Switzerland.</p>
<p>The energy of a particle in 3-dimensional space consists of its rest energy, $E=mc^2$, and the kinetic energy of its motion.
If extra dimensions do exist, then the particle will have extra space to move in, so will obtain an additional, independent contribution to its kinetic energy. Since we don't observe the motion of the particle in the extra dimension, this kinetic energy will be interpreted as rest energy, or in other words, the mass of the particle. </p>
<p>This is all understood perfectly fine, but it is this quote that comes next that confuses me:</p>
<blockquote>
<p>To us, the particle would not look like one particle, but a set of particles - all with different masses.</p>
</blockquote>
<p>Why would the particle look like a set of particles rather than just the one that is being observed?</p>
<p>Furthermore, why would they all have different masses?</p>
<p>How many particles would there be in this set?</p>
<p>Please keep your answers as simple as possible, as I am just a Layman.</p> | g10821 | [
0.06233035773038864,
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0.008900690823793411,
0.04164992645382881,
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0.04590676724910736,
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0.03189150616526604,
0.0018175438744947314,
0.0... |
<p>While studying quantum mechanics from standard textbooks I always felt some conceptual gap that was never mentioned or explained. In what follow I tried to formulate my question, please be patient with me.</p>
<p>For a quantum particle in an infinite potential well the stationary states are labelled by the quantum number $n$ which labels the eigenenergies. An eigenenergy, that corresponds to a stationary state, does not change with time, hence is a conserved quantity.</p>
<p>For a spinless electron in Coulomb potential, to model the hydrogen atom, again we have the same story, the stationary states are labeled by the quantum numbers $n$, $l$, $m$ which corresponds to conserved quantities.</p>
<p>My question is rather general since I am trying to understand conceptually why only conserved quantities are used to label the quantum states.</p>
<p>I mean how would someone think in advance that he has to look for conserved quantities, and then use such conserved quantities to label the states ? </p> | g10822 | [
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0.03471215441823006,
0.056686766... |
<p>Why different objects have different colour? When a white light (composed of all colour) falls on a red book, is it true that only red colour is reflected back? If no, then why it appears red. If yes, then why does the book doesn't get warmer even if it absorbed rest other wavelengths. How is hot red iron rod different than red book?</p>
<p>Kindly help in clearing this confusion. </p> | g10823 | [
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0.03788784518837929,
0.0318... |
<p>It has been claimed (e.g. <a href="http://physics.stackexchange.com/a/36178/10552">here</a>) and apparently already been established, that the interval $x - y$ being (called) "spacelike" implies that $\bigl[\hat O (x),\, \hat O' (y)\bigr]=0$ for any two (not necessarily distinct) operators $\hat O$ and $\hat O'$ corresponding to physical observables evaluated at $x$ or at $y$, respectively: </p>
<p>$$\text{spacelike}( \, x - y \, ) \quad\implies\quad \Bigl( \forall \hat O \, \forall \hat O': \Bigl[\hat O (x),\, \hat O' (y)\Bigr] = 0 \Bigr). $$</p>
<p>Is the converse correct, too, that the vanishing commutators imply (or are sufficient for) the interval $x - y$ to be (called) "spacelike":</p>
<p>$$\Bigl(\forall \hat O \, \forall \hat O': \Big[\hat O (x),\, \hat O' (y)\Bigr] = 0 \Bigr) \quad\implies\quad \text{spacelike}( \, x - y \, ) \, ?$$</p> | g10824 | [
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0.016656406223773956,
-0.014236771501600742,
0.007130416575819254,
0.027960188686847687,
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0.005290846340358257,
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0.019403792917728424,
0.026776790618896484,
0.0... |
<p>In a scanning electron microscopy, secondary electrons are defined as the electrons which obey inelastic scattering whereas backscattering electron follow elastic scattering. </p>
<p>Now my question </p>
<blockquote>
<p>Can backscatter electrons produce same level of solution as secondary electrons? </p>
</blockquote> | g10825 | [
0.04452171549201012,
0.029881324619054794,
0.018849534913897514,
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0.007506236899644136,
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0.06103375554084778,
-0.000993854831904173,
-0.03... |
<p>I think I have learned in physics that escape velocity is defined as the speed at which objects going ballistic in the opposite direction of the main gravitational force are able to finally overcome that force (assuming the simplest case with two directly opposing forces).</p>
<p>This means objects ballistically moving away from Earth slower than that velocity would never be able to escape and will finally fall back to Earth.</p>
<p>I have heard in many documentaries that this is the reason that spacecraft must accelerate to that velocity to get into deeper space at all.</p>
<p>However, as far as I understand it, spacecraft are not purely ballistic objects and could be controlled and accelerated step by step as needed, so why is it not possible to escape from Earth with lower speed and just "keep going", i.e. "accelerating" (exerting force) only to not come to a halt ?</p> | g10826 | [
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0.008168398402631283,
0.036279890686273575,
0.01954897865653038,
0.00699... |
<p>My understanding of weak gravitational lensing is that it assumes random alignment distribution of galaxies in order to estimate statistical shear and convergences, which are used to estimate matter distributions. This might be subject to noise that depends on the granularity and presence of galaxies, and the expected ellipticity of the galaxies.</p>
<p>matter sources will deflect light in several wavelengths in different amounts. Also, there are different backgrounds at different wavelengths that should be deflected consistently by real matter sources, specially dark matter.</p>
<p>Is such kind of multi-spectral, multi-background correlation analysis a standard procedure to validate dark matter concentrations? I'm particularly interested in the case of the Bullet Cluster, which is kind of <em>the</em> pivotal example to support dark matter.</p>
<p>For instance, CMB light should be deflected by dark matter just like far-away galaxies. I'm guessing without much knowledge about the subject that convergence of CMB is hard to estimate because it is mostly undistinguishable from thermal fluctuations (possibly with the exception of polarization of the CMB, which I won't discuss). But if we could correlate lensing/fluctuations of the CMB with galactic lensing (which is at different wavelengths, and at a different background), then one could in principle tell what features of the CMB are due to fluctuations and which one are due to actual lensing effects. Only real dark matter concentrations will persist across the spectrum and across the background. Measurement noise should be substantially reduced if done properly.</p>
<p>Does this analysis sounds accurate?</p> | g10827 | [
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0.047097347676754,
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0.012969017028808594,
0.06113... |
<p>I have always pictured <a href="http://en.wikipedia.org/wiki/Volume_element" rel="nofollow">volume element</a> as a small cuboid in with volume $dx dy dz$. however in <a href="http://en.wikipedia.org/wiki/Curvilinear_coordinates" rel="nofollow">curvilinear system</a>, how would the shape of this volume element be?</p>
<p>I mean in spherical polar coordinate system, how the shape of this volume element be visualized (is it a small sphere whose integration give the volume of object or same), or my idea of 3D Cartesian coordinate absolutely wrong.</p> | g10828 | [
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0.015582413412630558,
0.1093149408698082,
-0... |
<p>Is there a difference in <a href="http://en.wikipedia.org/wiki/Binet_equation" rel="nofollow">Binet's equation</a> when the force acting on a body is attractive and repulsive? </p>
<p>I mean, if the force has a magnitude $F(r)$, is it Binet's equation always $$\frac{d^2u}{d\theta ^2}+u=-\frac{F(u^{-1})}{mh^2u^2}, u=r^{-1},$$ no matter if the force is attractive or impulsive?</p> | g10829 | [
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0.005585090722888708,
0.02876098081469536,
0.04609347879886627,
-0.041525... |
<p>Can the vacuum be understood as a physical/chemical/material substance? </p>
<p>Remark: Vacuum has a density energy (so it has a density "mass" equivalence due to $E=mc^2$). Vacuum is quantum (but not classically!) polarizable (vacuum polarization effects are essential in QED or QCD).</p>
<p>Remark (II): A chemical substance is a form of matter that has constant chemical composition and characteristic properties.It can be solid, liquid, gas, or plasma. If vacuum is some kind of "substance" with some "physical" constant features (like density energy, polarizability,...), we can understand from elementary QFT principles that every particle is excitation from "a ground" state. Should we understand the SM as the vacuum composition or "states" at certain energy ranges ("temperature") just as a solid, liquid or gas (even a plasma) are just states at certain "temperature"?</p>
<p>Remark (III): Vacuum has "a structure" or "features" just as the state of matter show certain properties at certain temperatures. Is this just a useless analogy?</p> | g10830 | [
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0.03421453386545181,
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0.030407585203647614,
-0.021100124344229698,
0.035340458154678345,
-0.0034948757383972406,
0.017638660967350006,
... |
<p>How to prove that if a particle performs cyclical motion then its energy loss rate averaged over the period equals averaged radiation intensity?</p>
<p>The energy loss rate is the quantity of energy that the particle loses in unit time. And radiation intensity is an energy which observer detects some time later than it was emitted (due to finitude of light speed).</p>
<p>$$\frac{d E}{d t} = - \int d\Omega \left( 1 - \frac{(\vec n, \vec V(t))}{c}\right)\frac{dI(t)}{d\Omega}$$</p>
<p>where $\vec V(t)$ is the particle's speed, and $\vec n$ is unit vector on sphere $d \Omega$.</p>
<p>One can integrate it over time period $\int_{0}^{T}$ and get averaged energy loss rate $\langle\frac{d E}{d t}\rangle$, averaged intensity $\langle I\rangle$ and $$\int dt \int d\Omega \frac{(\vec n, \vec V(t))}{c}\frac{dI(t)}{d\Omega} $$ which should equals zero in order the initial sentence to be true.</p> | g10831 | [
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0.02799278497695923,
0.0... |
<p>Well, the difference between the two expressions $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is exactly $\Delta p^2$ , i.e. the squared uncertainty (variance) of the momentum,
where the $\hat p$ is momentum operator and uncertainty on the momentum operator is defined by:
$$\Delta p= \sqrt {\langle \hat p^2 \rangle_{\psi} - \langle \hat p \rangle_{\psi}^2}$$.
why the difference between $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is NOT zero?</p> | g10832 | [
0.030776159837841988,
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0.003210620954632759,
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-... |
<p>I've recently been working through a lot of physics problems and a lot of them say to assume that the mass of the string used in a problem involving a pulley, for example, is negligible. Why is this important? What would happen if the mass of the string wasn't negligible? </p> | g10833 | [
0.034484829753637314,
0.02567186765372753,
0.038626186549663544,
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<p>A container filled with fluid is accelerating initially with a1 and instantly changes to a2 (a2 < a1). What would happen to the fluid in the container. </p>
<p>My thoughts on this - If the velocity of the system is v1 when the acceleration changes to a2.
The fluid will, at that instant, have a velocity of v1 while container accelerates (with an accleration a2) to v2 (v2>v1) The fluid in the container is moving backwards relative to the container. So, it would splash against the back wall of the container. Is this logically accurate or am I missing something.</p> | g10834 | [
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0.0293206... |
<p>I wonder if someone can help me with the following problem.</p>
<p>I send a light beam to a distant galaxy which then bounces back to me.</p>
<p>I measure the travel time of the lightbeam using say a light clock of fixed size which I assume measures conformal time $\tau=\int dt/a(t)$.</p>
<p>Is the proper distance of the galaxy at the moment that I receive the lightbeam given simply by:
$$L = \frac{c\ \tau}{2}?$$</p> | g10835 | [
0.026486452668905258,
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<p>I was playing with some High-Voltage the other day, when a question popped into my head. Can you calculate length of an electrical arc? It probably would be proportional to :-<br>
1. Voltage of the source<br>
2. Spark gap<br>
3. Relative Humidity (in air only)<br>
4. Resistivity of Medium<br>
5. Shape of the Electrodes<br>
Can anyone come up with a dimensional formula from this...?</p> | g10836 | [
0.06822559982538223,
0.007105078082531691,
-0.0075690229423344135,
-0.03591427579522133,
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0.... |
<p>This photo was published at <a href="http://www.stern.de/bdt/bilder-des-tages-gefaehrliche-tropfen-1501450-4a50503e928f997c.html" rel="nofollow">stern magazine online</a>.
<img src="http://i.stack.imgur.com/Ryhyi.jpg" alt="contaminated water leaks out of vessel"></p>
<p>I wonder which information about the physical quantities could be reconstructed or computed given this photograph, the exposure time, and the detector size.</p>
<p>The white dots in the image correspond to particle traces on the imaging sensor. Thus by just counting the number of white dots, we know how many gamma photons interacted with the sensor while passing through. I will neglect the fact that the white pixels could also be caused by defect pixels aka "dead pixels". Let's assume the photo was taken with a non-stationary new camera. </p>
<p>So the only physical quantity I could come up is: </p>
<p>$$\frac{\text{# of white dots}}{12\pi \text{sr}\ \text{sensor_area}\cdot \text{exposure_time}}$$</p>
<p>Is there a way to find out more with some very conservative assumptions about the environment? What would these assumptions be?</p> | g10837 | [
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0.044267553836107254,
0.055665627121925354,
0.09355268627405167,
0.08339512348175049,
0.0057... |
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